Fractional diffusion: probability distributions and random walk models

We present a variety of models of random walk, discrete in space and time, suitable for simulating random variables whose probability density obeys a space–time fractional diffusion equation. Here we sketch our original approach to the topic that can o er some novel and inspiring inspections. In particular we pay attention to the fact that the fundamental solutions of the proposed fractional di usion equations provide spatial probability densities evolving in time, related to self-similar stochastic processes, that we view as generalized (or fractional) di usion processes to be properly understood through random walk models.